Methods for separation of polymeric compounds

ABSTRACT

Recently two techniques using free solution electrophoresis to separate charged-uncharged polymer conjugates have proven successful: End Labeled Free Solution Electrophoresis (ELFSE) for DNA sequencing, and Free Solution Conjugate Electrophoresis (FSCE) for molar mass profiling of uncharged polymers. Previous attempts have been made to analyze experimental data generated by these new techniques for the electrophoresis of molecules with varying charge distributions. However, the importance of the ends of the polymers in determining the polymer&#39;s overall mobility was neglected in previous work. Through a careful investigation and a reanalysis of the experimental data, it is determined here that this “end effect” critically impacts the behavior of polymers and charged-uncharged polymer conjugates during electrophoresis. In this way, the invention provides for methods that exploit this “end effect” for the separation of polymeric molecules on the basis of size, including for example DNA separation and sequencing techniques.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the priority right of prior U.S. patentapplication 60/615,600 filed on Oct. 5, 2004 by applicants herein.

GOVERNMENT INTERESTS

This invention was made in part with U.S. Government support under NIHGrant No. HG002918 and DOE Grant No. DE-FG02-99ER62789. The U.S.Government may retain certain rights in this invention.

FIELD OF THE INVENTION

The present invention relates to the field of polymer separation byelectrophoresis, in particular the separation of charged polymers byelectrophoresis. In particular, the invention relates to the field ofseparating polymers on the basis of size such as for examplepolynucleotides.

BACKGROUND TO THE INVENTION

In several areas of technology it is desirable to separate polymericcompounds on the basis of their size, configuration, charge or otherfundamental characteristics. For example, techniques relating tomolecular biology and biotechnology frequently involve the analysis of amixture of polypeptides or polynucleotides, which may be separated inaccordance with their relative sizes. Results can provide indication ofthe size and relative abundance of compounds in the mixture withsignificant accuracy. Indeed, some techniques enable the separation ofpolynucleotides with a resolution of a single nucleotide, which iscritical for analysis such as DNA sequencing.

Traditionally, compounds such as polypeptides and polynucleotides areseparated by electrophoresis involving the application of an electriccurrent through a buffered solution containing the compounds. During theelectrophoresis the compounds may be forced to migrate through a matrixmaterial that hinders progression of the migration. Such matrixmaterials may include agarose or polyacrylamide. Longer polymericcompounds migrate more slowly through the matrix when compared toshorter polymeric compounds, resulting in fairly rapid separation of thecompounds on the basis of polymer length.

More recently, much attention has been focused on the free-solutionelectrophoresis of charged-uncharged polymer conjugates in microchannelelectrophoresis systems such as capillary electrophoresis or microchipelectrophoresis systems. The performance of electrophoresis in freesolution overcomes the need for gels or entangled polymer solutions forthe electrophoretic separation of polyelectrolytes, while offering ameans for the molar mass profiling of uncharged polymers. End-labeledfree-solution electrophoresis (ELFSE), for instance, was successfullyused to sequence ssDNA up to 110 bases in less than 20 minutes [1]. Thistechnique cleverly uses an uncharged “label” or “drag” molecule attachedto each single-stranded DNA (ssDNA) chain in order to break the localbalancing between friction and electric force [2, 3, 4, 5, 6] whichnormally leads to co-migration of all ssDNA lengths [7, 8] (exceptingvery small fragments [9, 10]) in free solution. More recently, acomplementary technique called free solution conjugate electrophoresis(FSCE) has been used to characterize uncharged, water-soluble polymersthat can be uniquely conjugated to ssDNA [11, 12, 13]. Here the ssDNAchains are of uniform length, and act as engines to pull the varyinglengths of uncharged polymers for electrophoresis leading tosingle-monomer resolution over a wide range of molecular sizes. In fact,the resolution obtained was approximately five times higher, and theseparation efficiencies were increased by 150% compared to the moretraditional RP-HPLC [12]. For both FSCE and ELFSE, the theoreticalequation utilized for the overall mobility μ of the charged-unchargedblock copolymer was a uniformly weighted average [5, 6. 11, 13]:

$\begin{matrix}{\mu = {{\mu_{0}\frac{M_{c}}{N}} = {\mu_{0}\frac{M_{c}}{M_{c} + {\alpha_{1}M_{u}}}}}} & (1)\end{matrix}$where M_(c) is the number of charged monomers each of mobility μ_(c),and M_(u) is the number of uncharged monomers. This equation comes froma pioneer investigation of Long and co-workers into the electrophoresisof polymers containing both charged and uncharged monomers [14]. Thefactor α₁ rescales M_(u) account for the difference in hydrodynamicproperties arising for example from the different persistence lengths (ameasure of flexibility) of the charged and uncharged polymers. Hence theα₁ value depends on the chemistry of the molecules and varies with bothtemperature and buffer ionic strength (which affect the molecules'flexibilities). In fact, α=α₁M_(u) enables a counting of uncharged unitswhich have the same friction as one ssDNA monomer, such that the totalnumber of effective monomers is N=M_(c)+α₁M_(u). The α₁ value is animportant determinant of the mobility since the frictional drag of theuncharged polymer is what selectively slows down longer conjugates inFSCE, and determines the read length of ELFSE.

Therefore, it is generally known in the art that the modification ofpolynucleotides for example by the covalent attachment of selectedmoieties can increase the frictional ‘drag’ of the polynucleotide duringfree-solution electrophoresis.

The work of Long and coworkers, as well as the work of others, hasincreased our general understanding of the mechanisms of polymericcompound separation by free solution electrophoresis. Moreover, the useof tags to alter the frictional drag characteristics of oligonucleotidesduring free-solution electrophoresis has provided improvements in thesetechniques. Nonetheless, there remains a continuing need to developmethods for the separation of polymeric compounds that are simple,effective, and rapid. In particular there is a need to develop methodsfor the separation of polymeric compounds such as polypeptides orpolynucleotides with a high level of accuracy and a resolution of asingle amino acid or nucleotide.

SUMMARY OF THE INVENTION

It is an object of the present invention, at least in preferredembodiments, to provide a method for the separation of polymericcompounds.

It is another object of the present invention, at least in preferredembodiments, to provide a method for the separation of polymericcompounds with a resolution that permits differentiation of compoundsthat vary in size by only a few polymer units, or at least in morepreferred embodiments, by a single polymer unit.

It is another object of the present invention, at least in preferredembodiments, to provide a method of separating polymeric compounds thattakes advantage of the use of tags or covalently attached moieties toalter the frictional drag characteristics of the polymeric compound.

In one aspect of the present invention there is provided as method forseparating polymeric compounds according to their relative lengths, themethod comprising the steps of:

attaching a chemical moiety at or near each end of each of said linearpolymeric compounds to generate double end labeled polymeric compounds;and

subjecting the doubly end-labeled polymeric compounds to free-solutionelectrophoresis, each chemical moiety suitable to impart increasedhydrodynamic friction to each end of each double end labeled polymericcompound thereby to facilitate separation of the double end labeledpolymeric compounds according to their electrophoretic mobility duringsaid free-solution electrophoresis. Preferably, the polymeric compoundsare linear polymeric compounds. Preferably, the polymeric compounds arecharged polymeric compounds. Preferably, the chemical moieties areuncharged (or slightly charged) chemical moieties. Preferably, thepolymeric compounds are selected from polypeptides or polynucleotides.Preferably, the polymeric compounds are selected from, proteins, ssDNA,dsDNA and RNA.

In selected aspects, the chemical moieties are selected frompolypeptides, and polypeptoids (i.e., poly-N-substituted glycines). Inother aspects, the chemical moieties are selected from the groupconsisting of the protein Streptavidin, or a derivative thereof,N-methoxyethylglycine (NMEG) oligomers of length up to 300 monomer units(preferably up to 100 monomer units), and a molecule consisting of apoly(NMEG) backbone optionally with oligo (NMEG) branches.

In another aspect of the invention there is provided a method comprisingthe steps of:

(a) synthesizing a first plurality of ssDNA molecules each comprising asequence identical to at least a portion at or near the 5′ end of saidsection of DNA, said ssDNA molecules having substantially identical 5′ends but having variable lengths, the length of each ssDNA moleculecorresponding to a specific adenine base in said section of DNA;

(b) synthesizing a second plurality of ssDNA molecules each comprising asequence identical to at least a portion at or near the 5′ end of saidsection of DNA, said ssDNA molecules having substantially identical 5′ends but having variable lengths, the length of each ssDNA moleculecorresponding to a specific cytosine base in said section of DNA;

(c) synthesizing a third plurality of ssDNA molecules each comprising asequence identical to at least a portion at or near the 5′end of saidsection of DNA, said ssDNA molecules having substantially identical 5′ends but having variable lengths, the length of each ssDNA moleculecorresponding to a specific guanine base in said section of DNA;

(d) synthesizing a fourth plurality of ssDNA molecules each comprising asequence identical to at least a portion at or near the 5′end of saidsection of DNA, said ssDNA molecules having substantially identical 5′ends but having variable lengths, the length of each ssDNA moleculecorresponding to a specific thymine base in said section of DNA;

(e) attaching a chemical moiety to end nucleotides at or near each endof said ssDNA molecules to generate double-end labeled polymericcompounds; and

(f) subjecting each plurality of ssDNA molecules to free solutionelectrophoresis; and

(g) identifying the nucleotide sequence of the section of DNA inaccordance with the relative electrophoretic mobilities of the ssDNAs ineach plurality of ssDNAs;

wherein any of steps (a), (b), (c), and (d) may be performed in anyorder or simultaneously; and

whereby each chemical moiety imparts increased hydrodynamic friction toeach end of each double end labeled polymeric compound thereby tofacilitate separation of the double end labeled polymeric compoundsaccording to their resulting electrophoretic mobility.

Preferably, the chemical moieties are uncharged chemical moieties.Alternatively, in other preferred aspects the chemical moieties areselected from among polypeptides, and polypeptoids. Preferably, thechemical moieties are selected from the group consisting ofStreptavidin, or a derivative thereof, N-methoxyethylglycine (NMEG)oligomers comprising up to 300 (preferably up to 100) monomer units, anda molecule consisting of a poly(NMEG) backbone optionally with oligo(NMEG) branches.

Preferably, the section of DNA comprises less than 2000 nucleotides.More preferably, the section of DNA comprises less than 1000nucleotides. More preferably, the section of DNA comprises less than 500nucleotides. More preferably, the section of DNA comprises less than 300nucleotides. More preferably, the section of DNA comprises less than 100nucleotides.

In another aspect the invention provides for a method for separatingpolymeric compounds according to their relative size, the methodcomprising the steps of:

attaching a chemical moiety to each end of the polymeric compounds; and

subjecting the polymeric compounds to free solution electrophoresis.

Preferably, the difference in relative size of the polymeric compoundsis a single polymer unit.

Preferably, the polymeric compounds comprise DNA, and each polymer unitis a nucleotide.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1: End effect weighting function (Eq. (8)), an interpolatingfunction that provides a good fit of the numerical curve presented inFIG. 2 of [14]. The dotted line is the uniform weighting approximationthat was used in previous theoretical models [5, 6, 11, 13].

FIG. 2: Integral of end effect weighting function Ψ, from n=0 to M_(c),for FSCE with a charged ssDNA segment of M_(c)=20 bases plotted as afunction of the number M_(u) of monomers of PEG (α₁=0.138). Neglectingthe end effect would give a constant value of 20, indicated here by thehorizontal dashed line.

FIG. 3: Predicted arrival time at detector (scaled by the constant

$\left( {{scaled}\mspace{14mu}{by}\mspace{14mu}{the}\mspace{14mu}{constant}\mspace{14mu}\frac{L}{\mu_{0}E}} \right)$for FSCE with an M_(c)=20 ssDNA base engine plotted as a function of thenumber M_(u) of monomers of PEG (α₁=0.138). The solid curve is the casewith the end effect taken into account, the dotted line would beexpected were there no end effect. The lines cross at M_(u)=140 PEGmonomers in this example.

FIG. 4: Predicted peak sparing (scaled by the constant

$\left( {{scaled}\mspace{14mu}{by}\mspace{14mu}{the}\mspace{14mu}{constant}\mspace{14mu}\frac{L}{\mu_{0}E}} \right)$for FSCE with a) an M_(c)=20 ssDNA base engine, and b) an M_(c)=10 ssDNAbase engine, as a function of the number M_(u) of monomers of PEG(α₁=0.138). The solid curve is for the case with the end effect takeninto account, the dotted line would be expected were there no endeffect.

FIG. 5: Predicted arrival time at the detector for ELFSE, scaled by theconstant

$\frac{L}{\mu_{0}E},$as a function of the number M_(u) of uncharged monomers. The unchargeddrag molecule is of effective total size α=α₁M_(u)=36. The solid linerepresents the case with the end effect taken into account, the dottedline would be expected were there no end effect.

FIG. 6: Predicted ratio of ELFSE peak spacing with the end effect tothat expected without, for an uncharged drag molecule of effective totalsize α=α₁M_(u)=36 as used in [5, 6], as a function of the number M_(c)of charged monomers. Inset: predicted ratio of ELFSE peak spacing withthe end effect to that expected without, for an uncharged drag moleculeof effective total size α=α₁M_(u)=36 attached at both ends of the ssDNAas a function of the number M_(c) of charged monomers.

FIG. 7: Predicted ratio of ELFSE peak spacing for both ends of the ssDNAchain labeled with a drag of effective total size α=α₁M_(u)=36 to thatwith only one end labeled. Inset: predicted ratio of ELFSE peak spacing,taking into account the end effect, for a hypothetical uncharged dragmolecule of effective total size α=α₁M_(u)=100 to that of effectivetotal size α=α₁M_(u)=36, showing the higher peak spacing of the largerdrag molecule. Both curves were calculated by taking into account theend effect.

FIG. 8: Histogram of predicted arrival time (scaled by the constant

$\left( {{scaled}\mspace{14mu}{by}\mspace{14mu}{the}\mspace{14mu}{constant}\mspace{14mu}\frac{L}{\mu_{0}E}} \right)$to roughly show the expected peak shape without diffusion due to thevarious possible locations for a single deamidation of the ssDNA-proteinpolymer complexes (for which M_(u)=337 and M_(c)=23 before anydeamidation), investigated in reference [15]. We used α₁=1.

FIG. 9: Structures and code names for the six different drag-tagmolecules used in the experimental study. The P1-169 and P2-127drag-tags had maleimide functionalites added to their N-termini byactivation with Sulfo-SMCC, as described in Reference [24].

FIG. 10: T40-dithiol DNA (A) capped at both ends with excess maleimideto create unlabeled ssDNA, (B) mixed with a 15:1 molar excess of NMEG-40drag-tag followed by excess maleimide to create a mixture of unlabeledssDNA and ssDNA with one or two drag-tags, and (C) mixed with a 100:1molar excess or NMEG-40 drag-tag to create doubly labeled ssDNA. Sampleswere analyzed on an ABI 3100 capillary array instrument in 47 cmcapillaries (36 cm to detector) in 89 mM Tris, 89 mM TAPS, 2 mM EDTAbuffer, pH 8.5, with 1% v/v POP-6 polymer as a dynamic coating. Sampleswere injected electrokinetically at 22 V/cm for 3 seconds (A) or 2seconds (B and C), and run at a field strength of 320 V/cm, with acurrent of 15 μA per capillary.

FIG. 11: Capillary Electrophoresis (CE) analysis of mixtures of 20merand 40mer DNA with (A) NMEG-20 drag-tag, and (B) NMEG-40 drag-tag.Analysis conditions are the same as for FIG. 10, except the injectionwas 22 V/cm for 15 seconds. The running current was 15 μA per capillary.Peak assignments for both (A) and (B) are: 0=maleimide-capped DNA (nodrag-tag); 1=40mer DNA with one drag-tag; 2=2mer DNA with one drag-tag;3=40mer DNA with two drag-tags, 4=20mer DNA with two drag-tags.

FIG. 12: Electropherograms of dsDNA conjugated to P2-127 drag-tag. (A)100-bp PCR product with forward primer thiolated, (B) 100-bp PCR productwith both primers thiolated, (C) 200-bp PCR product with forward primerthiolated, and (C) 200-bp PCR product with both primers thiolated.Analysis conditions were the same as for FIG. 10, except the runtemperature was 25° C. and the injection was 1 kV for 20 seconds. Peakslabeled 0, 1, and 2 refer to DNA species with zero, one, or twodrag-tags, respectively.

FIG. 13: Total α=α₁M_(u) values calculated for different sizes M_(C) ofdsDNA with one (●) or two (▴) drag-tags. The horizontal lines show theaverage a values calculated from a linear fit of μ₀/μ vs. 1/M_(C), asgiven in Table 4.

FIG. 14 provides a flow diagram of a preferred method of the invention.

FIG. 15 provides a flow diagram of a preferred method of the invention.

DEFINITIONS

‘Drag’—whether used as a noun or as a verb, ‘drag’ refers to impedanceof movement of a molecule through a viscous environment (such as anaqueous buffer), such as for example during electrophoresis, either inthe presence or the absence of a sieving matrix.

ELFSE—End Labeled Free Solution Electrophoresis. The preferredconditions for ELFSE are apparent to a person of skill in the art uponreading the present disclosure, and the references cited herein

‘End effect’—refers to the increased weighting monomer units located ator near the end of a polymeric molecule subjected to ELFSE. In preferredembodiments the weighting may be the numerical function Ψ(n/N) given in[14]when represented, for example, by the following normalizedinterpolation function, shown in FIG. 1:Ψ(n/N)=−0.65+0.62/(n/N)^(1/4)+0.62/(1−n/N)^(1/4).  (3)

The inventors note that Ψ(n/N) increases substantially for monomerswithin about the first and last ˜8% of the chain (e.g., these sectionswould account for 24% of the total weighting of the molecule, comparedto the 16% expected by the uniformly weighted average approximation).Without wishing to be bound by theory, the inventors consider this aconsequence of monomers located close to the ends of the chain spendingmore time, on average, closer to the surface of the coil, and henceaffecting the overall mobility more than the middle monomers. As aresult the mobility is a weighted average of all individual monomermobilities, where monomers in die middle have approximately the sameweighting, but monomers near the end have a much greater weighting. Thisis the end effect which was neglected in previous ELFSE [5, 6] and FSCE[11, 13] analyses, where a uniform weighting, the dotted line in FIG. 1was taken as an approximation (see Eq. (1)).

EOF—Electroosmotic Flow

FSCE—Free Solution Conjugate Electrophoresis

‘Label’ or ‘tag’ or ‘drag-tag’: refers to any chemical moiety that maybe attached to or near to an end of a polymeric compound to increase thedrag of the complex during free solution electrophoresis, wherein thedrag is caused by hydrodynamic friction. In selected examples, the dragtag may comprise a linear or branched peptide or a polypeptoidcomprising up to 300, preferably up to 200, more preferably up to 100polymer units.

MALDI-TOF—Matrix-Assisted Laser Desorption/Ionization Time-of-Flight

‘Near’—In selected embodiments of the invention end labels are describedherein as being attached at or near to each end of a polymeric compound.In this context the term ‘near’ refers to attachment of a tag orchemical moiety to a monomeric unit in the vicinity of an end of thepolymeric compound, such that the presence of the moiety or taginfluences the “end effect” in accordance with the teachings of anddiscussions of the present application. In addition, the term “near” mayvary in accordance with the context of the invention, including the sizeanti nature of the moiety or tag, or the length and shape of thepolymeric compound. For example, in the case of a short polynucleotidecomprising less than 21) bases, the to term “near” may, for example,preferably include those nucleotides within 5 nucleotides from each endof the polynucleotide; However, in the case of a longer polynucleotidecomprising more than 100 bases then the term “near” may, for example,include those nucleotides within 20 nucleotides from each end of thepolynucleotide.

PEG—Poly(Ethylene Glycol)

‘Polymeric compound’—refers to any polymer whether of biological orsynthetic origin, that is linear or branched and composed of similar ifnot identical types of polymer units. In preferred embodiments, thepolymeric compounds are linear, and in more preferred embodiment thepolymeric compounds comprise nucleotides or amino acids.

‘Polypeptoid’—a linear or non-linear chain of amino-acids that comprisesat least one non-natural amino acid that is not generally found innature. Such non-natural amino acids may include, but are not limitedto, D-amino acids, or synthetic L-amino acids that are not normallyfound in natural proteins. In preferred embodiments, polypeptoids arenot generally susceptible to degradation by proteinases such asproteinase K, since they may be unable to form a protease substrate. Inselected embodiments, polypeptoids may comprise exclusively non-naturalamino acids. In further selected embodiments, polypeptoids may typicallybut not necessarily form linear or alpha-helical (rather than globular)structures. ‘Preferably’ and ‘preferred’—make reference to aspects orembodiments of the inventions that are preferred over the broadestaspects and embodiments of the invention disclosed herein, unlessotherwise stated.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Polymeric compounds, such as polypeptides and polynucleotides, areroutinely subject to modification. Chemical synthesis or enzymaticmodification can enable the covalent attachment of artificial moietiesto selected units of the polymeric compound. Desirable properties may beconferred by such modification, allowing the polymeric molecules to bemanipulated more easily. In the case of DNA, enzymes are commerciallyavailable for modifying the 5′ or 3′ ends of a length of ssDNA, forexample to phosphorylate or dephosphorylate the DNA. In another example,biotinylated DNA may be formed wherein the biotin moiety is located ator close to an end of the DNA, such that streptavidin may be bound tothe biotin as required. Tags such as fluorescent moieties may also beattached to polynucleotides for the purposes of conducting DNAsequencing, for example using an ABI Prism™ sequencer or otherequivalent sequencing apparatus that utilizes fluorimetric analysis

The inventors have undertaken a thorough investigation and review of thecapacity of covalently attached labels or tags to influence thefrictional drag characteristics of polymeric compounds, including forexample polynucleotides. Unexpectedly, the inventors have discoveredthat the covalent attachment of a label or tag at or near to both endsof a polynucleotide molecule can have a profound effect upon themobility and diffusion dynamics of the molecule during free solutionelectrophoresis. In some way, the presence of a tag or label at each endof the molecule results in an increase in drag to a greater extent thanwould be expected when considering the degree of drag generated bysingle end modification. Through careful analysis, the inventors havedelineated that this synergistic effect of double-end labeling is not anartifact or insignificant observation. Rather, it presents importantopportunities for the differentiation of molecules during free solutionelectrophoresis. Preferably the resolution is such that single polymerunits can be resolved, as would be required for example for DNAsequencing.

The methods of the invention involve End-Labeled Free-SolutionElectrophoresis (ELFSE) [1,3,4,16,17]. In preferred embodiments of theinvention, DNA is modified end-on with an uncharged, monodisperse,polymeric end-label or “drag-tag” to create a charged-uncharged polymerconjugate. During electrophoresis in free solution, the drag-tag impartsthe bioconjugate with a fixed amount of additional hydrodynamicfriction. The additional friction modifies the electrophoretic mobilityof the DNA-drag-tag conjugates in a size-dependent fashion: conjugatescomprising small DNA fragments migrate more slowly than conjugates withlarge DNA fragments, and thus a size-based separation can beaccomplished in the absence of a sieving matrix.

The theoretical principles and experimental demonstrations of ELFSE havebeen recently reviewed [17]. In the first experimental demonstration ofELFSE, streptavidin was used to label double-stranded DNA restrictionfragments that had been biotinylated at one or both ends [4]. Theefficiency of this separation was limited primarily by the inherentpolydispersity of the streptavidin label, as well as by interactionsbetween the streptavidin and the capillary walls. One of the interestingresults of this study, however, was that the amount of hydrodynamic dragassociated with adding a streptavidin label to both ends of the DNA wasobserved to be more than twice the friction for adding streptavidin toone end only. Whereas a single streptavidin provided friction equivalentto an additional 23 base pairs of DNA, two streptavidins provided thefriction of an additional 54 base pairs, 17% greater than would beexpected from simply doubling the amount of friction from a singlestreptavidin. The implications of this finding were not fullyappreciated at the time, and, being attributed to experimental error,this effect was not explored further.

The theoretical work of Long and co-workers [14] suggested that monomerunits at or near to the ends of a polymeric compound may contribute witha greater weighting to the compound's electrophoretic mobility (whencompared to other monomeric units). However, the previous practical workof the inventors, and others, has typically employed uniformly weightedaverages as an approximation for the mobility of the monomer unitswithin the test polymers. These studies neglected to take into accountcertain second-order effects, and in particular the so-called “endeffect” discussed above. While the qualitative results for the range ofdata treated with the approach of Long et al. were fairly good forcertain molecular sizes, the inclusion of the end effect into the theorymakes significant changes for the quantitative results, and how thetheory can be utilized. In particular, the inventors of the presentinvention demonstrate herein that the previously utilized approximationwould have resulted in unrealistic molar mass profiles had it beenapplied to a different range of polymer sizes. Hence the end effect mustbe carefully accounted for when using for example FSCE for molar massprofiling of synthetic uncharged polymers. The inventors successfullyapply the addition of the end effect to the theories of free solutionconjugate electrophoresis and end-labeled free solution electrophoresis.More importantly, the inventors provide strong evidence that double endlabeling (i.e. labeling of both ends of a polymeric compound) can giveparticularly desirable results in the separation of compounds byfree-solution electrophoresis.

The standard theory of ELFSE has been developed through investigationsinto the electrophoretic mobility of polymers with non-uniform chargedistributions. For the case of the migration of a DNA-drag-tagconjugate, with a charged DNA segment consisting of M_(C) chargedmonomers, and an uncharged drag-tag consisting of M_(U) unchargedmonomers, the mobility μ is traditionally given by a weighted average ofthe electrophoretic mobilities of the charged and uncharged monomers:

$\begin{matrix}{\mu = {\mu_{0}\frac{M_{C}}{M_{C} + {\alpha_{1}M_{U}}}}} & (2)\end{matrix}$where μ₀ is the mobility of the charged monomers (i.e. the free-solutionmobility of DNA). (The uncharged monomers have zero electrophoreticmobility, and thus do not appear in the numerator of Equation (2)). Theparameter α₁ re-weights the number of uncharged monomers M_(U) toreflect differences in persistence length and other hydrodynamicproperties. The product α₁M_(U), referred to as α, describes the totalfriction provided by the drag-tag, in terms of the number of additionaluncharged monomers of DNA that would add equivalent friction. Thus, inthe experiments described previously [4], a single streptavidin drag-tagprovided α=23, i.e. an amount of friction equivalent to 23 uncharged bpof DNA, whereas two streptavidins gave α=54. Notably, Equation (2)cannot adequately explain the more than doubling of α arising from usingtwo drag-tags.

Whereas previous theory assumed that each monomer unit (after resealingthe uncharged monomers by α₁) contributes equally to the electrophoreticmobility of the composite molecule, more recent theory has taken intoaccount end-effects originally described by Long et al. [14]. Accordingto this theory, monomer units near either end of the polymer chain havegreater influence than monomer units near the middle in determining theelectrophoretic mobility of the composite molecule. This can beexpressed by including a weighting factor Ψ in the calculation of themobility. For the case of ELFSE, with M_(C) charged monomers conjugatedend-on to M_(U) uncharged monomers, and scaling M_(U) by the factor α₁such that the total number of monomers is effectively N=M_(C)+α₁M_(U),the weighted average mobility is expressed as:

$\begin{matrix}{\mu = {\frac{1}{N}{\int_{0}^{M_{C}}{\mu(n)\mspace{11mu}\Psi\mspace{11mu}\left( \frac{n}{N} \right)\;{\mathbb{d}n}}}}} & (3)\end{matrix}$where the index of integration, n, represents the position of a chargedmonomer unit in the chain. The ratio n/N, which appears as the argumentof the weighting function Ψ, ranges from 0 to 1, and represents therelative position of a given monomer unit in the chain. The limits ofintegration are written from 0 to M_(C) (rather than 0 to N) since theuncharged monomers (n=M_(C)+1 . . . N) have zero electrophoreticmobility, and only the charged monomers contribute to the total. Makingthe further substitution that for charged DNA monomers, the mobilityμ(N)=μ₀, and using the definition N=M_(C)+α₁M_(U) the mobility of thecomposite molecule can be written as:

$\begin{matrix}{\mu = {\frac{\mu_{0}}{M_{C} + {\alpha_{1}M_{U}}}{\int_{0}^{M_{C}}{{\Psi\left( \frac{n}{M_{C} + {\alpha_{1}M_{U}}} \right)}\ {\mathbb{d}n}}}}} & (4)\end{matrix}$The normalized weighting function Ψ(n/N) of a Gaussian polymer chain wasfound by the inventors to be well-represented by the following empiricalfunction:

$\begin{matrix}{{\Psi\left( \frac{n}{N} \right)} \approx {{- 0.65} + {0.62\mspace{11mu}\left( \frac{n}{N} \right)^{- \frac{1}{4}}} + {0.62\mspace{11mu}\left( {1 - \frac{n}{N}} \right)^{- \frac{1}{4}}}}} & (5)\end{matrix}$Equation (5) is a well-behaved, easily calculated (and easilyintegrated) function for 0<(n/N)<1, and is depicted in FIG. 1 of thepresent application (see Examples). Using this functional form inEquation (4) allows the straightforward calculation of theelectrophoretic mobility for any composite molecule consisting of a DNAchain linked end-on to an uncharged drag-tag chain, provided that thescaling factor α₁ is known for a given set of experimental conditions.

For the slightly more complicated case of a charged DNA chain withuncharged drag-tags at both ends of the DNA chain, Equations (3) and (4)need only be modified by changing the limits of integration, and thetotal number of effective monomer units N. For the case of a DNA chainconsisting of M_(C) charged monomers, with identical drag-tagsconsisting of M_(U) uncharged monomers at each end, the total number ofeffective monomers is now N=M_(C)+2α₁M_(U). With this change, andinserting the appropriate limits of integration, the mobility becomes:

$\begin{matrix}{\mu = {\frac{\mu_{0}}{M_{C} + {2\alpha_{1}M_{U}}}{\int_{a_{1}M_{U}}^{{a_{1}M_{U}} + M_{C}}{{\Psi\left( \frac{n}{M_{C} + {2\alpha_{1}M_{U}}} \right)}\ {\mathbb{d}n}}}}} & (6)\end{matrix}$

Besides providing a more complete analysis of the electrophoreticmobility of ELFSE conjugates, and improving the quantitative analysis ofprevious data from the molar mass profiling of poly(ethylene glycol)[11], the theory of end-effects makes useful predictions for enhancingthe performance of DNA sequencing and other separations using ELFSE. TheΨ(n/N) function in Equation (5) has its maxima near the ends of themolecule, indicating that the chain ends are weighted more heavily indetermining the electrophoretic mobility of the composite molecule. Theheavier weighting of the chain ends implies that adding an unchargeddrag-tag to each end of a DNA molecule provides more than twice the dragof using a single drag-tag of the same size at one end of the DNAmolecule. This is consistent with the initial experimental observationsusing streptavidin as a drag-tag [4]. Moreover, since the production ofvery large, totally monodisperse drag-tag molecules has thus far beenproblematic [15, 24], the inventors demonstrate herein that the effectcan be exploited to provide sufficient drag for high-efficiencyseparations by using two smaller (and more monodisperse) drag-tags,rather than one larger drag-tag. The present invention providesexperimental confirmation of this effect using both short ssDNA oligosand larger dsDNA PCR products, with drag-tags of varying sizes at one orboth ends of the DNA molecules.

In its broadest embodiment, the invention relates to the modification ofany type of polymeric compound by presence of or the addition of asuitable label or tag at or near to both ends of the compound, whereinthe polymeric compounds are separated by free solution electrophoresis.Any type of polymeric compound may be modified in accordance with themethods of the present invention, including non-biological andbiological polymeric compounds. More preferably the compound is chargedin a manner that is suitable for separation by electrophoresis.Preferably, the tags or labels are not charged such that they merely actto cause drag upon the charged polymeric compound duringelectrophoresis. More preferably, the polymeric compound comprises alinear series of polymer units, such as for example in DNA.

The polymeric compound is preferably a polypeptide or a polynucleotide.More preferably the polymeric compound is a polynucleotide and themethod of the present invention is suitable to separate thepolynucleotide from other polynucleotides of differing size. Moreover,the polynucleotide may comprise any type of nucleotide units, andtherefore may encompass RNA, dsDNA, ssDNA or other polynucleotides.

In a more preferred embodiment of the invention, the polymeric compoundis ssDNA, and the methods permit the separation of compounds that areidentical with the exception that the compounds differ in length by asingle nucleotide or a few nucleotides. In this way the methods of thepresent invention, at least in preferred embodiments, permit theseparation and identification of the ssDNA products of DNA sequencingreactions. The size of the tag or label positioned at each end of thessDNA molecules is (at least in part) a function of the read length ofthe DNA sequencing that one may want to achieve. With increasing size oflabels or tags the inventors expect the methods of the present inventionto be applicable for sequencing reactions wherein a read length of up to2000 nucleotides is achieved. With other tags or labels shorter readlength may also be achieved including 300, 500, or 1000 base pairs. Thedesired read lengths will correspond to the use to which the DNAsequencing is applied. For example, analysis such as single nucleotidepolymorphism (SNP) analysis may require a read length as small as 100nucleotides, whereas chromosome walking may require a read length aslong as possible, for example up to 2000 base pairs.

Each tag or label may take any form of sufficient configuration or sizeto cause a sufficient degree of drag during free-solutionelectrophoresis. For example each label or tag may be a substantiallylinear, alpha-helical or globular polypeptide comprising any desiredamino acid sequence. Moreover, each label or tag may comprise anyreadily available protein or protein fragment such as an immunoglobulinor fragment thereof, Steptavidin, or other protein generated byrecombinant means. In a preferred embodiment each label or tag may be apolypeptoid comprising a linear or branched arrangement of amino acidsor other similar units that do not comprise L-amino acids andcorresponding peptide bonds normally found in nature. In this way thepolypeptoid may exhibit a degree of resistance to degradation underexperimental conditions, for example due to the presence of proteinasessuch as Proteinase K.

The attachment of each label or tag to the polymeric compound may occurby any suitable synthetic or enzymatic means, and may be conducted viathe use of commercially available systems and kits. For example, auseful way to modify both ends of a ssDNA molecule may include the useof thiol chemistry. However, any other suitable synthetic chemistry maybe used.

The invention will be further illustrated with reference to thefollowing examples, which are in no way intended to limit the scope ofthe invention.

EXAMPLES Example 1 Analysis of the Theory of Electrophoresis ofPolyampholytes

As previously discussed, the electrophoretic behaviour of polymers withinhomogeneous charge distributions was previously investigated by Longand co-workers [14]. The mobility of such chains was calculated as afunction of charge distribution, taking into account both hydrodynamicinteractions and the elasticity of the chain. They investigated thelinear regime of small electric fields where the polymer chains remainin approximately Gaussian conformation, and assumed excluded volumeeffects to be negligible. For uniformly charged polymers, thecounter-ions effectively cancel the long range hydrodynamic interactionsbetween monomers, such that hydrodynamic and electric forces arebalanced locally, leading to the well known “free-draining” phenomenonwhere uniformly charged polymers migrate at the same electrophoreticvelocity despite their varying lengths [7, 8]. However withnon-uniformly charged polymers, it was shown that hydrodynamicinteractions can play a large role. The general expression for theelectrophoretic mobility of a polymer with a variable chargedistribution was given as

$\begin{matrix}{\mu = {\int_{0}^{N}{{\psi(n)}{\mu(n)}\ {\mathbb{d}n}}}} & (7)\end{matrix}$where μ(n) is the mobility of the n^(th) monomer, and N is the totalnumber of monomers. The weighting function ψ(n) is universal forsufficiently long polymers, i.e. it looks the same for all sizes Nbeyond about ten persistence lengths in that ψ(n)=1/NΨ(n/N). Theinventors found that the numerical function Ψ(n/N) given in [14] isrepresented quite well by the following normalized empiricalinterpolation function, shown in FIG. 1:Ψ(n/N)=−0.65+0.62/(n/N)^(1/4)+0.62/(1−n/N)^(1/4).The inventors note that Ψ(n/N) increases substantially for monomerswithin the first and last ˜8% of the chain (e.g., these sections wouldaccount for 24% of the total weighting of the molecule, compared to the16% expected by the uniformly weighted average approximation). This is aconsequence of monomers located close to the ends of the chain spendingmore time, on average, closer to the surface of the coil, and henceaffecting the overall mobility more than the middle monomers. As aresult the mobility is a weighted average of all individual monomermobilities, where monomers in the middle have approximately the sameweighting, but monomers near the end have a much greater weighting. Thisis the end effect which was neglected in previous ELFSE [5, 6] and FSCE[11, 13] analyses, where a uniform weighting, the dotted line in FIG. 1was taken as an approximation (see Eq. (1)). This effect may indeed beof importance when analyzing data for charged-uncharged blockco-polymers, especially if one of the blocks is relatively small (e.g.,less than 10% of the total polymer length) and hence has a weightingdetermined solely by one of the “ends” of the curve in FIG. 1.

Example 2 Analysis of the End Effect for FSCE

For the case of FSCE, where only the M_(c) charged monomers have anon-zero mobility, one can rewrite Eq. (7) as follows:

$\begin{matrix}{\mu = {\int_{0}^{M_{c}}{\frac{\mu(n)}{N}{\Psi\left( \frac{n}{N} \right)}\ {\mathbb{d}n}}}} & (9)\end{matrix}$where the monomers are labeled starting from the charged end of thechain. The mobility of the n^(th) monomer μ(n), is simply thelength-independent free solution ssDNA mobility μ₀, and the effectivetotal number of monomers N is M_(c)+α₁M_(u) as before in the uniformlyweighted average, such that

$\begin{matrix}{\mu = {\mu_{0}\frac{\int_{0}^{M_{c}}{{\Psi\left( \frac{n}{M_{c} + {\alpha_{1}M_{u}}} \right)}\ {\mathbb{d}n}}}{M_{c} + {\alpha_{1}M_{u}}}}} & (10)\end{matrix}$

On comparison with Eq. (1) it is clear that taking the end effect intoaccount involves replacing the numerator (M_(c)) with the integral of Ψover all the charged monomers (i.e. replacing the uniform weighting ofΨ=1 which would give

∫₀^(M_(c))Ψ 𝕕n = M_(c),with the Ψ function of FIG. 1). As one can expect from the form of the Ψfunction, in going from a molecule that is completely charged to onethat is attached to an uncharged chain, the higher relative weighting ofone of the charged ends is lost and hence the end effect is manifestedby an initial drop in the integral of Ψ as M_(u) increases. However asthe uncharged segment grows quite large, the proportion of the conjugatemolecule which is charged (M_(c)/N) decreases significantly, and theweighting for each of the charged monomer mobilities is determinedsolely by the remaining higher end weighting. Consequently, as theuncharged segment becomes much larger than the charged segment, thelatter is given a higher weighting in the average determining the totalmobility, thereby increasing the mobility over that expected byneglecting the end effect. This is indeed what is seen in FIG. 2 whenthe integral of Ψ is plotted for the specific case studied by Vreelandet al. [11] of a 20 base ssDNA fragment (M_(c)=20) attached to variouslengths of poly(ethylene glycol) (PEG), for which α₁ was estimated to beapproximately 0.138 (to be discussed later). The integral in themobility equation initially decreases for small PEG molecules, and thenincreases for the larger molecules. This factor grows well beyond thevalue of 20 previously taken as an approximation (neglecting endeffects). For the longest PEG chains examined by Vreeland et al, whichhave a molecular mass of about 24 kDa (corresponding to about 550monomers), we estimate that the integral of Ψ is about 24, significantlyhigher than the previous approximation of 20.

The mobility of the conjugates varies not only with the weighting of theengine, but also with the total size: clearly molecules with largeruncharged segments move more slowly (this is the very means ofseparation). We take the mobility from Eq. (10) to find the arrival timeof the molecule at the detector:

$\begin{matrix}{t = {\frac{L}{\mu_{0}E} \times \frac{M_{c} + {\alpha_{1}M_{u}}}{\int_{0}^{M_{c}}{{\Psi\left( \frac{n}{M_{c} + {\alpha_{1}M_{u}}} \right)}\ {\mathbb{d}n}}}}} & (11)\end{matrix}$where L is the length to the detector, and E is the electric fieldintensity. FIG. 3 shows how the arrival time (scaled by the constant

$\frac{L}{\mu_{0}E}$which is the elution time of naked ssDNA, i.e. for molecules withM_(u)=0) depends on the end effect. When the end effect is neglected, wesee a straight line (as reported by Vreeland et al. [11] for narrowranges of PEG molecular size). However, taking into account the endeffect results in a slightly higher slope for very small PEG segments,which decreases as the size of the PEG grows, becoming significantlyless than it would be were the end effect not at play. As expected, theend effect gives a higher weighting to the charged engine such thatmolecules (having more than 140 PEG monomers in this example) go fasterthan if the end effect is neglected, and increasingly so for largerconjugates where the engine weighting is pushed further to the left onFIG. 1. Unfortunately this increased speed has a negative impact onseparation: for the same separation length L and field intensity E, themolecules have less time for their differences in speed to slow onerelative to another. The predicted temporal peak spacing

$\frac{\partial t}{\partial M_{u}}$is shown in FIG. 4 for both an ssDNA engine size of M_(c)=20, and one ofsize of 10, which was previously predicted to be the optimal engine size[13]. Without end effects we would expect a horizontal line (one of themore interesting features of FSCE); however with end effects we see thatpeak spacing decreases with increasing conjugate size. For the largermolecules studied by Vreeland et al. (around 550 monomers conjugated toa 20 base DNA engine), we estimate that the end effect reduces the peakspacing to only 63% of that expected were there no end effect (see FIG.4 a). This decrease is even more pronounced for shorter chargedsegments; for an engine size of M_(c)=10 (FIG. 4 b), the inventorspredict that the peak spacing for the larger molecules would drop to amere 54% of that previously expected. Note that even though the endeffect plays a more detrimental role for the shorter engine, the overallpeak spacing is still higher. As well, it should be noted that forconjugates with small uncharged segments, the end effect could beexploited as it actually leads to an important increase in separationunder these conditions.

Here the inventors illustrate the manifestation of the end effect in thepublished FSCE experimental data [11], which previously went unnoticed.The decrease in the slope of arrival time (FIG. 3) is slow, hence over asmall range of sizes the size-dependence of the arrival time couldeasily appear to be linear; this was indeed what Vreeland et al.reported [11]. The measured arrival times were linear for both PEGmolecular size ranges, the smaller sizes ranging from approximately 4.5kDa through 7 kDa (corresponding to about M_(u)=100 through 160 PEGmonomers) and the larger ranging from about 20 kDa through 24 kDa (aboutM_(u)=450 through 550 PEG monomers). As previously mentioned, theapproach taken for the data analysis was to neglect the end effect byassuming the Ψ weighting function to be uniform (see Eq. (1)). Hence byneglecting the Ψ dependence on α₁M_(u), this term could be isolated fromthe mobility expression,

${\alpha_{1}M_{u}} = {M_{c}\left\lbrack {\frac{\mu_{0}}{\mu} - 1} \right\rbrack}$and plotted as a function of peak number (which varies linearly with thenumber of PEG monomers M_(u) since FSCE yields single monomerresolution). The slope of this plot, which is basically a scaled arrivaltime, was then simply taken to be α₁. This value was then used tocalculate the molar masses of both samples since it should not depend onthe length of the polymers, rather just their individual monomer lengthsand flexibilities. As we can see from FIG. 3, while the slopes of thearrival times with and without the end effect taken into account divergefor larger PEG sizes, they are fairly similar for M_(u)≈100-160monomers. Hence the approximation used to determine α₁ from the data byneglecting the end effect may be reasonable for these small sizes;however one would expect it to be poor for the larger sizes for whichthe end effect has a more critical impact. Fortunately, when theapproximation of neglecting the end effect was used [11], α₁=0.138 wasin fact determined using only the small sizes range (M_(u)≈100-160monomers) and then this value was used to calculate the molar massprofiles for all sizes. As a result of this somewhat lucky choice forthe size range to determine α₁, very good agreement with MALDI-TOFanalyses of molar masses was achieved; for example, FSCE gave a (number)average molar mass of M_(n)=5735 g/mol, while MALDI-TOF, the industrystandard, gave M_(n)=5728 g/mol for the small sizes range [11]. In fact,for all PEG sizes conjugated to an engine of 20 bases, FSCE molar massesagreed with MALDI-TOF results to within a 3.2% difference, supportingthe use of the α₁ value of 0.138 determined from the small sizes. Ifhowever one had used the FSCE data for the larger PEG sizes(M_(u)≈450-550 monomers) to determine α₁ under the approximation ofneglected end effects, good results would not have been achieved. FIG. 3suggests that the slope of the arrival time for these larger sizes issignificantly less than expected by neglecting the end effect. Hence theα₁ value obtained by this approximation, i.e. from the scaled arrivaltime slope, would be expected to be less than that of the small sizes.Using the approximation of neglected end effect to determine α₁ from thelarger sizes would have lead to erroneous molar mass calculations fromFSCE data, i.e. M_(u)=9652 g/mol instead of M_(n)=5728 g/mol fromMALDI-TOF, for the small sizes range. This means a 69% difference,compared to the mere 0.12% difference from using the α₁ value determinedfrom the smaller PEG sizes for which the end effect plays a lesser role.Clearly the end effect has a critical impact on the electrophoreticbehaviour of charged-uncharged polymer complexes and must be taken intoaccount to ensure accurate determinations of molar mass from FSCEanalysis.

In the preceding development the inventors chose to use α₁=0.138 due tothe good agreement achieved between FSCE and MALDI-TOF results; howeverwe could also determine a value for both α₁ and M_(u) simultaneously bysolving the equation for arrival time (Eq. (11)) and its derivative withrespect to M_(u). By this approach we take the end effect into accountand use only the arrival time of the conjugates at the detector and thederivative of this time with respect to peak number. (Note that the peaknumber varies linearly with PEG size M_(u), as mentioned previously.)This system of two equations and two unknowns was solved numerically toyield values of α₁=0.168 and M_(u)=111 monomers for the middle peak ofthe small PEG sizes (5 kDa nominal average molar mass). The results forthe midpoint of the larger PEG sizes (20 kDa nominal average molar mass)were also fairly reasonable at α₁=0.129 and M_(u)=560 monomers. The α₁values determined by this technique have a percent difference of 23% (asopposed to 69% using the previous approach). One possible reason for theremaining discrepancy is that experimental conditions may have changedeither between runs with the shorter and larger PEGs or even during asingle run. The larger PEGs take about 3 times longer to elute and henceit is possible that the electric current may drop and/or the temperaturemay change slightly during the course of the experiment, for example. Achange in temperature would change the value of α₁ directly since thisvalue depends on the flexibility of the polymers, which in turn dependon temperature. If there were a drop in current between the time whenthe mobility of the unconjugated engine μ₀, is measured and when themobility of the conjugates μ, are measured then these two values wouldnot correspond to the same conditions as expected by Eq. (10). While theend effect is clearly manifested in the FSCE data, there is still somediscrepancy between prediction and that which is observedexperimentally; this may be due to changes in experimental conditionssuch as those mentioned above, or to second order effects not yet takeninto account which will be discussed later.

Example 3 Analysis of the End Effect for ELFSE

With ELFSE, variable engine (ssDNA) lengths M_(c) are conjugated touncharged molecules of a set size M_(u). In previous experimental work[5, 6, 1], the uncharged drag molecule was streptavidin, which wasestimated (by neglecting the end effect) to have an effective number ofmonomers α₁M_(u)=36 under the specific experimental conditions. Throughconjugation with the uniform drag molecules, the various lengths ofssDNA, up to about 110 bases, were successfully sequenced in freesolution [1]. Since ELFSE is used for sequencing of DNA, an exact valuefor alpha is not as crucial for data analysis, i.e. one need only beconcerned with the sequence of arrival times, which is not changed bythe end effect. However, to fully understand ELFSE data, and to makepredictions for optimal sequencing conditions, the role that the endeffect plays should be addressed.

The arrival time at the detector for ELFSE is given by Eq. (11), as withFSCE; here however the engine size M_(c) is no longer constant, ratherit is the uncharged segment that remains fixed. As the engine growsrelative to the drag molecule, the region of the Ψ curve determining itsweighting expands beyond the “end” weighting to encompass more of thelower weighting of the “middle” (see FIG. 1). In FIG. 5 it can be seenthat the end effect speeds up smaller molecules, while it slows downlarger molecules. Again we are mostly concerned with the resolution,which depends in part on peak spacing. The end effect is expected todecrease peak spacing for the range of data previously investigated(below 110 bases); however it should start to increase peak spacing atabout 115 monomers. This crossover from a negative impact on peakspacing to a positive one is shown by the ratio of predicted peakspacing with the end effect taken into account to that without; see FIG.6. For 110 bases, there is a slight decrease in peak spacing expecteddue to end effects, which will quickly be replaced toy a positive effectfor larger sizes. Hence this examination of the end effect bodes wellfor ELFSE as this technique matures, i.e. by increasing separatingcapacity for larger molecules over what could be expected based on datafor shorter molecules, where end effects had a more pronounced negativeeffect.

One of the goals of current ELFSE work is to increase the size of theuncharged segment of the conjugate so as to increase the frictional dragit induces and extend the read-length, i.e. the number of bases whichcan be sequenced. Unfortunately for a larger “drag” molecule of 100(rather than 36) effective monomers, the end effect would be expected todecrease peak spacing up until about 320 monomers, i.e. a crossover froma negative to positive effect at about 320 instead of 115 monomers.However, despite the farther reaching negative impact of the end effect,the greater friction of a larger drag molecule would nevertheless resultin better separation. The predicted ratio of peak spacing for thehypothetical drag molecule of 100 effective monomers to that of 36effective monomers is shown in the inset of FIG. 7. The peak spacing issignificantly higher for the larger label, at least two times higherthroughout the range of DNA sizes shown.

In any event, the inventors reasonably expect that the methods of thepresent invention may be applied to DNA sequencing reactions such that aread length of at least 500, preferably 1000, preferably 2000nucleotides may be achieved. In this way, the methods of the inventionmay be applied to a wide range of applications where DNA sequencing isrequired, whether a short or longer read length is preferred.

Example 4 Labelling Both Ends of ssDNA for ELFSE

Another means of increasing the resolution of ELFSE would be to labelboth ends of the ssDNA chain with the drag molecule. This would thusgive each conjugate two drag molecules, thus increasing the totalfriction; however in contrast to simply doubling the size of a singledrag molecule, the key feature of this configuration is that the dragmolecules would be given the highest weighting, that of both ends,leaving the charged section only the lower “Middle” weighting of the Ψfunction. Hence by placing the uncharged sections, with their nullmobility, at each end, the resulting frictional drag of the conjugate isoptimized; adding one label to each end of the ssDNA chain has moreimpact than doubling the size of a single end label. FIG. 7 shows theexpected peak spacing improvement when both ends are labeled with thedrag molecule of 36 effective monomers rather than just one. Clearly,having two drag molecules instead of one does not simply double theeffective friction coefficient of the uncharged sections as would beexpected were there no end effect, rather it increases it by a factorgreater than two due to the end effect. One important finding is that,unlike the situation with only one end label, the end effect increasespeak spacing for all sizes when both ends are labeled (see the inset ofFIG. 6). For smaller ssDNA chains, having both ends labeled with a dragmolecule of 36 effective monomers results in better peak spacing thanhaving a single drag molecule of 100 effective monomers, whereas forlarger chains, beyond 308 bases, the inverse is true (compare FIG. 7with its inset). Since it may be difficult to find a larger dragmolecule which is suitable (i.e. it would have to be water soluble andamenable to uniform conjugation to ssDNA), it may be preferable toattach two of the smaller labels as a means of improving ELFSEseparation; this is one of the main findings of this work. Previously,Heller et al. [4] labeled double stranded DNA with a streptavidinmolecule on one end as well as both ends. By neglecting the end effect,Heller et al. interpreted their experimental results by calculating avalue of α for these conjugates to be 23 for a single drag molecule, but54, rather than 46. for two drag molecules. Heller et al. provide littleor no discussion of this result, and presumably attribute theseexperimental observations to an artifact or standard errors. While theseresults were misunderstood at the time, a detailed theoreticalre-analysis of the data of Heller et al. by the inventors of the presentinvention, indicates that the end effect did in fact play a significantrole in determining the overall mobility of the conjugates; labelingboth ends more than doubled the effective friction coefficient, a resultthat could not be explained until now.

Example 5 Discussion of Examples 1-4

It is important to note that the end effect theory of Long andco-workers [14] is for random Gaussian coils. The end effect arises dueto the effective “shielding” of monomers located inside the coil (onaverage) which leaves the ends (located closer to the outside of thecoil on average) to interact more with the surrounding fluid, andthereby to have a greater effect on the overall mobility. Hence one mustbe careful in applying the results presented herein to very shortmolecules whose conformation may not yield this end effect. Also, forvery large molecules, there is an excluded volume effect that is notaccounted for by the random Gaussian coil approximation, which couldchange the predictions somewhat for these larger molecules.

There is also a small effect due to the hydrodynamic interactionsbetween adjacent monomers on the chain which was not taken into accountin previous theories. Although long-range hydrodynamic interactions arescreened by the counter-ions, there is some coupling on a local scalebetween adjacent monomers [14]. As a result, uncharged monomersneighbouring charged monomers are pulled along by the hydrodynamic flowcreated by the electrophoretic pull on the charged monomers. This effectis highly localized and drops off exponentially with distance, howeverit gives an effective non-zero mobility to nearby uncharged monomers.This highly localized effect also means that the end monomers of acharged section have a slightly lesser effective mobility than those inthe middle of the charged section since they do not have the additionalmobility due, to the hydrodynamic flow created by the electrophoreticmovement of the nearby charged monomers on both sides. Hence for themobility in FSCE and ELFSE, the more highly weighted monomers, the onesat the end, have a slightly lesser effective mobility, while the firstfew uncharged monomers near the joint with the charged chain sectionhave a slight, non-zero mobility. Hence this local hydrodynamic effectcould play a role in determining the overall mobility of conjugates; forexample, it could decrease the end effect slightly by decreasing themobility of the more heavily weighted monomers, those charged monomersat the end of the molecule. However this would be in an absolute fashionin that it would not depend on the relative sizes of the differentcomponents of the molecule, unlike the end effect. For ssDNA under theconditions of ELFSE and FSCE however, the extra mobility given to theuncharged segment neighboring the ssDNA monomers, and that taken awayfrom the first few ssDNA monomers on each end of the ssDNA segment, areexpected to be negligible. However, for more flexible molecules thislocal hydrodynamic coupling extends over more monomers and hence thiseffect could be important and in preferred embodiments may be taken intoconsideration for the mobility of such conjugate molecules.

The inventors' re-analysis of the FSCE results, in light of the endeffect predicted by Long and co-workers [14] has shown that this effectis indeed significant; it is readily visible in the data and must betaken into account when calculating the molecular mass. As the size ofthe uncharged polymers increases, the relative size of the enginedecreases so that it receives a much greater weighting in the averagedetermining the overall mobility. As a result, for larger molecules thepredicted mobility is greater than would be expected were there no endeffect. There is a corresponding decrease in peak spacing, originallyassumed to be constant [11, 13], which must be taken into account whenanalyzing the data, especially when the peak spacing is used todetermine the α₁ value (if the uncharged polymer. In previous work [11,13] the inventors were fortunate to use the peak spacing for the smallerPEG molecules to determine the value of α₁ that was then used todetermine the molecular masses, because the end effect had less of animpact for the smaller sizes, such that the approximation of negligibleend effects was acceptable. The value of α₁ used in the determination ofthe molecular masses from FSCE data is crucial and unfortunately can notbe obtained as simply as previously thought. It can be calculated fromthe persistence lengths and monomer sizes of the two sections of theconjugate [13], although one would need to be careful to take theexperimental conditions (temperature and ionic strength) into account.Another means of determining the α₁ value would be to compare the FSCEresults to MALDI-TOF results for the same polymer and find the α₁ valuethat allows for agreement between the two molecular mass estimates(similar to the approach taken in this paper for assessing the accuracyof the value for α₁). This value need only be determined once for eachconjugate type and then FSCE calculations can be made independently. Inaddition, the simultaneous solution of the equations for the arrivaltime and the derivative of the arrival time provides another means ofestimating α₁. For this technique to yield accurate results, a veryprecise measurement must be made of the length-independent free solutionssDNA mobility μ₀, as the results obtained depend quite sensitively onit. It may be best to inject unconjugated ssDNA molecules periodicallythroughout the migration time of the conjugates so as to monitor anychanges in this value due to changes in experimental conditions duringthe experiment.

Although the end effect explains the decrease in peak spacing observedin FSCE data, it does not appear to completely account for the decrease.This effect is predicted (based on an α₁ value of 0.138) to decrease thepeak spacing of the larger PEG sizes (about 500 monomers) to 77% of thatof the smaller PEG sizes (about 130 monomers), whereas the data shows agreater decrease: the peak spacing of the larger PEG sizes is only 59%of that for the smaller PEG sizes. This discrepancy may be due toexcluded volume effects for the larger PEG sizes which were neglected byLong and co-workers when they determined the function governing the endeffect [14]. Also any variation in temperature or electric currentduring or between experiments would change the mobility, and the formerwould also lead to a change in persistence length, thereby changing the≢₁ value itself. A very clear demonstration of the decrease in peakspacing for larger molecules is provided by Bullock [18], where PEG withtwo end labels were electrophoresed in free solution. The end labelingwas achieved by reacting the terminal hydroxyl groups of PEG withphthalic anhydride, thereby tagging a phthalate ester onto each end. Theseparation was performed under conditions of electroosmotic flow (EOF),such that there was a strong electric field driven counter-flow thatcaused the molecules to migrate backwards in the electric field suchthat the slowest became the fastest and vice versa. The change in peakspacing with molecule size is readily visible in the electropherogram,FIG. 11 in [15]; the larger PEG molecules (about 70 monomers) have apeak spacing that is less than one fifth of that of the smaller PEGmolecules (about 20 monomers). Not only does this show a very clear,single data set expression of decreased peak spacing for largerconjugates, but it also confirms that the decrease in peak spacing isnot due to a systematic change in experimental conditions duringelectrophoresis causing a decrease in peak spacing because here the EOFmakes it such that the larger molecules elute first.

The end effect is also very important for ELFSE since it can greatlyincrease, or reduce peak spacing depending on the conditions of theexperiment. Once the desired sequencing length is chosen, the end effectcan be taken into account in order to determine the necessary labelconfiguration. The end effect is predicted to increase peak spacing formolecules just beyond the range of current experimental data [1], andhence affects predictions of optimal performance. Having a precise valuefor α₁ is not as much of an issue as it is for FSCE because with ELFSEthe ssDNA is being sequenced and hence the length is known. This valuemay be important however for system optimization and other theoreticalanalyses; for example the inventors have found that attaching the smalllabel (of effective size 36) that has been used experimentally thus far,to both ends of the ssDNA would result in better peak spacing than couldbe achieved through one single larger label (of effective size 100),under certain conditions. This remarkable result could not have beenexpected without taking the end effect into account.

The end effect not only has a critical impact on the electrophoreticbehaviour of charged-uncharged polymer complexes, but it also affectspolymers with variable charge distributions. Due to the end effect, apolymer having more of its charges located near the end(s) would have ahigher electrophoretic mobility than if its charges were located at themiddle of the chain. Recently a technique similar to FSCE was used tostudy glutamine deamidation in a long polypeptide [16]. The extent towhich glutamine deamidation occurs varies with the extent of exposure tocyanogen bromide cleavage reaction mixture. In order to assess thedegree of deamidation, a uniform DNA engine was conjugated to theprotein polymer for electrophoresis. The latter however, was also of aset length, but it had a varying charge distribution due to the negativecharge of the deamidated glutamic acid residue(s). In this study therewere 48 potential sites for deamidation spaced evenly throughout theprotein polymer and it was assumed that deamidation occurred randomlyover these sites. The electrophoretic separation revealed varyingelectrophoretic mobilities even though the complexes were all of thesame length, because of the varying extents of deamidation: the greaterthe extent of deamidation, the greater the charge and hence the higherthe mobility. However, for each degree of deamidation the end effectwould also result in a spread in mobilities based on the location of thedeamidation site along the chain. Even for a single negative chargeresulting from a single deamidation, the 48 possible locations for thecharge, some near the end, others near the middle of the conjugate,would allow for a spread in mobilities. This spread is due to a constantvelocity difference between the molecules with different deamidationlocations, and hence the peaks would be expected to broaden linearlywith time even in the absence of diffusion. The peak shape for a singledeamidation is roughly predicted to be that presented in FIG. 8. Thisrough peak shape was obtained by approximating α₁=1, and taking themobility of a deamidated glutamic acid residue to be about that ofsingle-stranded DNA. Each location for the negative charge due todeamidation is expected to have equal probability. To obtain theexpected peak shape we used a histogram that would collect the number ofconjugates arriving at the detector within a set amount of time. Clearlythere are some conjugates that have a much higher mobility (and henceshorter arrival time); these faster molecules have their deamidationinduced negative charge located near the end of the chain and hence theend effect gives it a greater weighting in the mobility. These fastermolecules may even be lost in the peak corresponding to the next levelof deamidation. This may explain some of the peak shapes observed in[16]. Hence the end effect may also be of interest in analyzingelectropherograms of uniform length molecules with varying chargedistributions.

Example 6 Chemicals and Drag-Tag Molecules

In the subsequent examples, the following chemicals and drag-tagmolecules were utilized:

Tris(2-carboxyethylphosphine) (TCEP) and maleimide were purchased fromAcros Organics (Morris Plains, N.J., USA). Sulfosuccinimidyl4-N-maleimidomethyl cyclohexane-1-carboxylate (Sulfo-SMCC) was purchasedfrom Pierce (Rockford, Ill., USA). Buffer salts Tris (free base),N-tris[hydroxymethyl]methyl-3-aminopropanesulfonic acid (TAPS), and EDTAwere purchased from Amresco (Solon, Ohio, USA). POP-6 polymer solutionwas purchased from Applied Biosystems (Foster City, Calif., USA). Allwater was purified using an E-Pure system from Barnstead (Boston, Mass.,USA) to a minimum resistivity of 17.8 MΩ-cm.

Six different drag-tag molecules were used in the subsequent examples.Three were linear N-methoxyethylglycine (NMEG) oligomers of length 20,40, or 44 monomers, produced by a solid-phase submonomer syntheticprotocol [19], capped with an N-terminal maleimide, and purified tomonodispersity by RP-HPLC as described previously [12, 20, 21]. Anotherdrag-tag used was a monodisperse branched molecule consisting of a 30merpoly(NMEG) backbone with five octamer oligo (NMEG) branches, alsodescribed previously [22]. The final two drag-tags were repetitiveprotein polymers of length 127 and 169 amino acids, produced using thecontrolled cloning technique [23], and activated at the N-termini usingthe heterobifunctional crosslinker Sulfo-SMCC by reacting the proteinpolymers with a 10-fold molar excess of Sulfo-SMCC for one hour at roomtemperature and pH 7.2, and then removing excess crosslinker by gelfiltration as described previously as described previously [24, 15]. Thestructures and short names of the drag-tags are shown in FIG. 9. TheNMEG-20 and NMEG-40 drag-tags were used for the studies of ssDNA,whereas the larger tags were used for the studies of dsDNA. All of thedrag-tags used are hydrophilic, water-soluble molecules. Following themaleimide activation of the N-termini, the NMEG drag-tags arecharge-neutral, whereas the P1-169 has a net charge of −1 (fromdeprotonation of the C-terminus), and the P2-127 (with two cationicarginine residues) has a net charge of +1.

Example 7 Production of ssDNA Conjugates

Two poly(dT) oligonucleotides of length 20 and 40 bases were purchasedfrom Integrated DNA Technologies (Coralville, Iowa, USA). The oligoswere modified at the 5′ end with a thiol linker that has a 6-carbonspacer, and at the 3′ end with a thiol linker having a 3-carbon spacer.The oligos were also modified internally with a fluorescein-dT base nearthe middle of the chain. These dithiolated, fluorescently labeled oligos(referred to as T20-dithiol and T40-dithiol) are shown schematically inTable 1.

TABLE 1 Oligonucleotides used for producing ssDNA conjugates withdrag-tags at one or both ends. X₁ = 5′-thiol linker with 6-carbonspacer, X₂ = internal fluorescein-dT base, X₃ = 3′ -thiol linker with3-carbon spacer. Oligonucleotide Sequence T20-dithiol X₁ TTTTTTTTTX₂TTTTTTTTTT X₃ T40-dithiol X₁ TTTTTTTTTT TTTTTTTTTX₂ TTTTTTTTTTTTTTTTTTTT X₃

The thiol linkers on the DNA oligos were reduced using TCEP. Toaccomplish this reduction, 400 pmol of the dithiolated ssDNA (eitherT20-dithiol or T40-dithiol) was mixed with a 40:1 molar excess of TCEP,in a total volume of 10 μL of sodium phosphate buffer (100 mM, pH 7.2).This mixture was incubated at 40° C. for 2 hours. The reduced DNA wasthen split into aliquots of 10 pmol each prior to the addition of thedrag-tag. To one aliquot, a large excess of maleimide (5 nmol) wasadded, capping the reduced thiols, and creating ssDNA molecules with nodrag-tag (except the maleimide). To another aliquot, a large excess ofdrag-tag (1 nmol of either NMEG-20 or NMEG-40) was added, such that themajority of ssDNA molecules would have polymeric drag-tags at both ends.The other aliquots were treated with different amounts of drag-tag, from50-200 pmol, with the intent of creating mixtures containing appreciableamounts of DNA with zero, one, or two drag-tags. After reacting forapproximately 90 minutes, an excess of maleimide (5 nmol) was added tothese reactions to cap any remaining free thiols. The reactions wereincubated in the dark at room temperature for at least four hours priorto CE analysis.

Example 8 Production of dsDNA Conjugates

Oligonucleotides used as PCR primers were purchased from Integrated DNATechnologies, and are shown schematically in Table 2.

TABLE 2 Oligonucleotides used as PCR primers for producing dsDNAconjugates with drag-tags at one or both ends. X₁ = 5′-thiol linker with6-carbon spacer, X₂ = internal fluorescein-dT base. OligonucleotideSequeuce M13-Forward X₁ CCX₂TTTAGGG TTTTCCCAGT CACGACGTTG 75-ReverseGAGTCGACCT GCAGGCATGC 75-Reverse-T X₁ GAGTCGACCT GCAGGCATGC 100-ReverseGAGCTCGGTA CCCGGGGATC 100-Reverse-T X₁ GAGCTCGGTA CCCGGGGATC 150-ReverseGCGGATAACA ATTTCACACA 150-Reverse-T X₁ GCGGATAACA ATTTCACACA 200-ReverseCCAGGCTTTA CACTTTATGC 200-Reverse-T X₁ CCAGGCTTTA CACTTTATGCThe oligonucleotides consist of an M13 forward primer with a 5′-thiollinker and an internal fluorescein-dT base, and a set of M13 reverseprimers, with or without 5′-thiol linkers, designed to produce dsDNAproducts of 75, 100, 150, or 200 bp in size when used in a PCR reactionwith the forward M13 primer.

PCR reactions were performed using Pfu Turbo polymerase (Stratagene, LaJolla, Calif., USA). Eight reactions were carried out with 20 pmol ofthe fluorescently labeled, thiolated M13 forward primer, and 20 pmol ofeach of the M13 reverse primers shown in Table 2, in a total volume of20 μL. M13 control DNA from a sequencing kit (0.2 μL) (AmershamBiosciences, Piscataway, N.J., USA) was used as a template. The M13template was PCR-amplified with 32 cycles of denaturation at 94° C. for30 seconds, followed by annealing at 54° C. for 30 seconds and extensionat 72° C. for 60 seconds. Products were analyzed by 2.5% agarose gelelectrophoresis to confirm the sizes of the dsDNA amplicons, and theproducts were stored at −20° C. until subsequent use.

Thiolated PCR products were reduced using a large excess of TCEP. To dothis, 7 μL of PCR product was mixed with 0.7 μL of 1M TCEP (in 1M Trisbuffer), plus an additional 0.35 μL of 1M Tris, resulting in a solutionof pH ˜5. This mixture was incubated for 2-2.5 hours at 40° C. ExcessTCEP as well as PCR reaction components were removed using QIAquick PCRpurification spin columns (QIAgen, Valencia, Calif., USA) according tothe manufacturer's instructions, with elution of the purified DNA in 30μL of 100 mM sodium phosphate buffer, pH 7.2.

The purified PCR products (with one or two reduced thiols, depending onthe reverse primers used) were split into multiple aliquots, and treatedwith one of four maleimide-activated drag-tags: NMEG 44 branchedNMEG-70, P1-169, or P2-127. The amounts of drag-tag were sufficient inmost cases to produce significant quantities of DNA with one or twodrag-tags. Additional aliquots were treated with excess maleimide, tosimply cap the reduced thiols and prevent further reaction ordimerization.

Example 9 CE Analysis of Conjugates

Free-solution CE analysis was performed using an Applied BiosystemsPrism 3100 Genetic Analyzer (Applied Biosystems, Foster City, Calif.,USA), using an array of 16 fired silica capillaries with inner diameterof 50 μm, and a total length of 47 cm (36 cm to the detector). Therunning buffer was 89 mM Tris, 89 mM TAPS, 2 mM EDTA, pH 8.5, and 1% v/vPOP-6 polymer solution to act as a wall-coating agent, with the adsorbedpoly(dimethylacrylamide) effectively suppressing the electroosmotic flow[25]. (The resulting polymer concentration is very low, and does notlead to any size-based sieving of the DNA.) samples were diluted inwater prior to analysis, to provide signals of appropriate strength forthe fluorescence detector. The ssDNA samples were analyzed at 55° C.,whereas dsDNA samples were analyzed at 25° C. to prevent denaturation.Samples were introduced into the capillaries by electrokinetic injectionat 1 kV (22 V/cm) for 2-20 seconds. Separations were carried out at 15kV (320 V/cm). The fluorescein label of the DNA was detected in the “G”channel of ABI Dye Set E5, with λ_(max)≈530 nm.

Example 10 Analysis of ssDNA Conjugates

The experimental protocol in which ssDNA was mixed with differentamounts of maleimide-activated drag-tag allowed the successfulproduction of species with zero, one, or two drag-tags, which wereeasily separated and identified by free-solution CE analysis. This isillustrated in FIG. 10 for the case of the T40-dithiol DNA with NMEG-40drag-tags. As seen in FIG. 10A, DNA with no drag-tag eluted as a singlesharp peak with an electrophoretic mobility μ₀=3.9×10⁴ cm²/V·s. Adding a5- to 20-fold molar excess of the drag-tag to the DNA resulted inmixtures containing significant amounts of DNA with zero, one, or twodrag-tags, as shown in FIG. 10B. Adding the drag-tag in a much largermolar excess (100-fold, relative to the DNA) led to nearly completereaction of both ends of the DNA, again resulting in a single sharp peakas seen in FIG. 10C. Residual TCEP, present at 40-fold excess during thereduction, interferes somewhat with the reaction of the free thiols withthe maleimide-activated drag-tags, and it was found that a significantlygreater than 40-fold molar excess of drag-tag was necessary to achievecomplete derivatization of both ends of the DNA. Species that wereidentified as ssDNA with one drag-tag typically appeared as a doublet ofclosely-spaced peaks, as with the middle peak in FIG. 10B. The reasonfor this was not immediately obvious, but one possibility is that slightdifferences in electrophoretic mobility arise from labeling at the5′-end or 3′-end of the DNA molecule, since the thiol linkers at the twoends are of different lengths.

In the optimized protocol, excess maleimide was used to cap anyremaining unreacted thiols. We did this because, in initial attempts toproduce mixtures comprising significant amounts of DNA with zero or onedrag-tag, additional peaks would appear at characteristic spots in theelectropherogram, particularly between the peaks for DNA with one andtwo drag-tags, and trailing the peak for DNA with two drag-tags. Theextra peaks would be absent when the samples were first analyzed, butwould grow in magnitude over the course of hours to days after thereduction of the DNA and reaction with the drag-tags. Although the extrapeaks were never conclusively identified, it was hypothesized that theyresulted from re-oxidation of some of the residual free thiols to formdisulfides. The addition of excess maleimide about two hours after theaddition of the drag-tag effectively prevented this problem, as themaleimide rapidly reacts with any remaining free thiols. The capping ofboth ends of the dithiolated DNA with this small molecule was found toinduce a small, almost negligible mobility shift of 2-3 seconds relativeto reduced, uncapped dithiolated DNA, corresponding to an additionaldrag for the maleimide moiety equivalent to ˜0.1 bases of DNA.

For each drag-tag (NMEG-20 or NMEG-40), samples consisting of both sizesof DNA (T20-dithiol or T40-dithiol) with zero, one, or two drag-tagswere pooled to create mixtures containing multiple species, which werethen separated and analyzed by CE. Run-to-run and capillary-to-capillaryvariabilities in migration time were generally quite low (approximately±1%), allowing easy identification of peaks in the pooled samples bycomparing to the migration times of the individual components prior topooling. CE analyses of these pooled mixtures are shown in FIG. 11,along with the peak assignments. A simple visual inspection confirms thegeneral predictions of the end-effects theory: 20mer DNA with two 20merdrag-tags (FIG. 11A, Peak 4) elutes later than 20mer DNA with one 40merdrag-tag (FIG. 11B, Peak 2), and likewise for the 40mer DNA (compare11A, Peak 3 and FIG. 11B, Peak 1).

For the case of the migration of a DNA-drag-tag conjugate, with acharged DNA segment consisting of M_(C) charged monomers, and anuncharged drag-tag consisting of M_(U) uncharged monomers, the mobilityμ is traditionally given by a weighted average of the electrophoreticmobilities of the charged and uncharged monomers:

$\begin{matrix}{\mu = {\mu_{0}\frac{M_{C}}{M_{C} + {\alpha_{1}M_{U}}}}} & (2)\end{matrix}$where μ₀ is the mobility of the charged monomers (i.e. the free-solutionmobility of DNA). (The uncharged monomers have zero electrophoreticmobility, and thus do not appear in the numerator of Equation (2)). Theapparent overall frictional parameter α=α₁M_(U) (as given by Equation(2)) could be computed directly from the peak times in FIG. 11.

The α value calculated through use of Equation (2), which neglects theend-effect, is termed the “apparent” a value so as to distinguish itfrom that determined using other equations which account for theend-effect. The apparent α values, which qualitatively display the trendexpected from the end-effects theory, are shown in Table 3.

TABLE 3 Apparent frictional parameter α for ssDNA with one or twodrag-tags calculated from peak times in FIG. 11, with correction madefor the slight mobility shift arising from the maleimide capping. Thefinal column gives the ratio of the drag for a tag at each end versusthe expected drag for a single tag of twice the size. Error margins onexperimentally determined α values assume an uncertainty of ±0.05minutes in peak times, which reflects the run-to-run andcapillary-to-capillary variability observed with the instrument. Ratio[α₍₂₎/ DNA length Drag-tag Apparent α Error (±) 2α₍₁₎] 20 NMEG-20 (one)5.1 0.07 1.07 NMEG-20 (two) 10.9 0.1 20 NMEG-40 (one) 9.7 0.1 1.09NMEG-40 (two) 21.2 0.2 40 NMEG-20 (one) 6.1 0.08 1.06 NMEG-20 (two) 12.90.2 40 NMEG-40 (one) 11.2 0.2 1.09 NMEG-40 (two) 24.5 0.3

It is evident that two drag-tags give more than double the drag of asingle tag, with roughly 6-9% enhancement for two drag-tags on ssDNAversus the expected drag for a single tag of twice the size. Theseexperimental results will be analyzed quantitatively below, using themore detailed theory taking end-effects into account.

It is also clear from the results in Table 3 that the apparent a for agiven size of drag-tag depends on the size of the DNA. For example, twoNMEG-20 drag-tags on the 20mer DNA give α=10.9, whereas the same twoNMEG-20 drag-tags on the 40mer DNA give α=12.9—a difference of 18%. Thisis in agreement with the end-effects theory: for a drag-tag of a fixedsize on one or both ends, a longer DNA molecule means that the drag-tagmonomers are relatively closer to the chain end (n/N closer to 0 and/or1), thereby giving the drag-tag monomers a heavier weighting indetermining the mobility of the conjugate. Thus, the apparent α valuefor a given drag-tag on one or both ends of the DNA increases as the DNAchain length increases.

Example 11 Analysis of dsDNA Conjugates

Double-stranded DNA conjugate molecules were produced by performing PCRusing a thiolated forward primer and normal (unthiolated) reverse primer(for production of dsDNA conjugates with a drag-tag at one end only), Orusing thiolated forward and reverse primers (for production of dsDNAconjugates with drag-tags at both ends). A large excess of TCEP was usedfor reduction of the thiols after the PCR reaction. Since TCEP issupplied as an HCl salt, the use of a large excess results in anacidification of the PCR buffer. To compensate for this, and to preventlong-term exposure of the DNA to very acidic conditions, additional 1 MTris was added to the reduction mixture, resulting in a more acceptablepH. Following the reduction, the PCR products were purified usingQIAquick spin columns, which effectively remove residual buffer salts,surfactants, enzyme, and reducing agents left over from the PCR reactionand reduction, which might otherwise interfere with reaction with thedrag-tags.

The drag-tags used for the dsDNA conjugates were two moderately largesynthetic polypeptoids (linear NMEG-44 and branched NMEG-70), and twoprotein polymers produced by genetic engineering of E. coli. Thebranched NMEG-70 and the P1-169 drag-tags have been described previouslyfor the separation of denatured (single-stranded) PCR products of sizessimilar to those described here [22, 24]. In this study, CE analysis wasperformed at room temperature with no denaturants in the buffer,ensuring that the DNA remained in its double-stranded state. Keeping theDNA in its double-stranded state allows for the easy incorporation of adrag-tag at both ends, which was expected to generate more than twicethe drag of a single drag-tag, allowing the separation of a wider sizerange of dsDNA molecules.

The concentration of the DNA purified with the QIAgen spin column wastoo low for accurate measurement of absorbance at 260 nm, and thus themolar ratios of DNA to drag-tag are not known precisely. The amounts ofdrag-tag were generally sufficient to produce significant amounts ofproduct with zero and one drag-tag (for products with only the forwardprimer thiolated), and zero, one, and two drag-tags (for PCR productswith both primers thiolated). Typical electropherograms for two sizes ofDNA (100 bp and 200 bp) with the P2-127 protein polymer are shown inFIG. 12. In each case, the “free” DNA (with no drag-tag) elutes around6.2 minutes. In panels (A) and (C), which show PCR products generatedwith only a thiolated forward primer, the “free” DNA peak is followed bya single peak, corresponding to DNA with a single drag-tag. In panels(B) and (D), which show PCR products generated with both forward andreverse thiolated primers, there is an additional peak eluting 1-2minutes later, corresponding to DNA with a drag-tag at both ends. Notealso in panels (B) and (D) that, for the products generated with bothprimers thiolated, there are two closely spaced peaks eluting around thesame time as the product with one drag-tag in panels (A) and (C). Aswith the split peaks for the ssDNA conjugates with one drag-tag, theexact cause of this phenomenon is unknown, but it was observed for allsizes of dsDNA with all of the drag-tags, and may result from slightdifferences in electrophoretic mobility arising from labeling at eitherend of the DNA molecules.

The P1-169 and P2-127 protein polymers used here as drag-tags were notentirely monodisperse [24], leading to some additional peak broadness.The additional broadness is most noticeable with the smaller sizes ofDNA, and is more pronounced for the species with two drag-tags. Both ofthese effects are as expected. Sharper peaks for larger sizes of DNAconjugated to impure drag-tags (including P1-169) were reported in [24],and are also in line with theory presented in Reference [26]. Theconjugation of a polydisperse drag-tag to both ends of a DNA moleculeleads to a large number of possible combinations, earth with slightlydifferent electrophoretic mobility, which is apparent as additional peakbroadness. The NMEG-44 and branched NMEG-70 drag-tags, both of whichwere purified to near monodispersity by RP-HPLC, generate cleaner,sharper peaks than the protein polymer drag-tags.

Alpha values were calculated from the peak elution times of eachspecies, and are plotted versus the DNA size M_(C) in FIG. 13. Inprevious ELFSE literature, the relative mobilities of unlabeled andlabeled DNA (μ₀/μ) would be plotted with respect to 1/M_(C), resultingin a straight line with slope α [1, 4]. This approach neglects theend-effects theory, which predicts a different overall value of α foreach size of DNA. In this case, such plots are still essentially, linear(not shown), and can be used to give an average apparent value of α foreach drag-tag. These average α values are given in Table 4, and are alsodrawn as horizontal lines in FIG. 13. (Note that the average a valuesdetermined by the linear fit of μ₀/μ versus 1/M_(C) are not necessarilyequal to the arithmetic average of the individual α values calculatedfor each size of DNA.) As indicated by the right-most (“Ratio”) columnin Table 4, the average α for two drag-tags is noticeably greater(10-23%) than twice α for a single-drag-tag, for these dsDNA species.

TABLE 4 Apparent frictional parameter α for dsDNA with one or twodrag-tags, averaged for all sizes of DNA. The final column gives theratio of the drag for a tag at each end versus the expected drag for asingle tag of twice the size. Drag-tag Average α Ratio [α₍₂₎/2α₍₁₎]NMEG-44 (one) 12.7 1.10 NMEG-44 (two) 28.0 Branched NMEG-70 (one) 17.01.22 Branched NMEG-70 (two) 41.6 P1-169 (one) 27.2 1.13 P1-169 (two)61.7 P2-127 (one) 19.9 1.23 P2-127 (two) 48.8

Example 12 Discussion of Examples 6-11

The results obtained for the analysis of ssDNA conjugates withpoly(NMEG) drag-tags can be compared directly to the predictions fromthe end-effect theory presented in Equations (4) and (6). To take theend-effect into account, the weighting function presented in Equation(5) is used. The parameter α₁ for scaling the uncharged monomers can becalculated using the end-effect theory, but we must first account forthe slight additional drag arising from the maleimide moiety added tocap any unreacted thiols. To find the drag α_(m) associated with asingle malcimide cap, the following equation was solved (using Maple):

$\begin{matrix}{t = \frac{t_{0}\left( {M_{c} + {2\alpha_{m}}} \right)}{\int_{\alpha_{m}}^{\alpha_{m} + M_{c}}{{\Psi\left( \frac{n}{M_{c} + {2\alpha_{m}}} \right)}\ {\mathbb{d}n}}}} & (12)\end{matrix}$where t₀ is the arrival time of the uncapped DNA, and t is the arrivaltime of the DNA capped on each end with maleimide. For the 20-base DNA,α_(m) was found to be 0.035, while for the 40-base DNA it was found tobe 0.052. Since the end-effect theory was derived for long Gaussianchains, it is assumed that the α_(m) value found for the larger DNAchain more closely represents the true value.

Note that the fluorescein-dT base near the middle of the chain likelyexerts some effect on the mobility, as the fluorescein carries a −2charge, and the dye along with the spacer arm linking it to the dT baselikely add some hydrodynamic friction. To properly account for thiseffect would require a dithiolated oligonucleotide with no fluorescein,which would be undetectable with the CE instrument used for theanalysis. The effect of the fluorescein is likely moderated by itsposition near the middle of the DNA chain (and hence its lower weight indetermining the electrophoretic mobility). Additionally, theexperimental determinations of a were made by comparing mobilities ofdrab-tag-labeled and “free” DNA, all of which were labeled identicallywith fluorescein. The impact on the results is expected to be minimal,and thus the contributions of the fluorescein as well as the thiollinkers present on all of the DNA species are ignored.

For DNA with one drag-tag and one maleimide cap, α₁ for the drag-tag canbe found by solving Equation (13):

$\begin{matrix}{t_{1} = \frac{t_{0}\left( {M_{c} + \alpha_{m} + {\alpha_{1}M_{u}}} \right)}{\int_{\alpha_{m}}^{\alpha_{m} - M_{c}}{{\Psi\left( \frac{n}{M_{c} + \alpha_{m} + {\alpha_{1}M_{u}}} \right)}{\mathbb{d}n}}}} & (13)\end{matrix}$where t₀ is the arrival time of the DNA with no drag-tag (aftercorrecting for the presence of maleimide caps on each end), and t₁ isthe arrival time of the DNA with one maleimide cap and one drag-tag. Thecalculated values of α₁ are presented in Table 5.

TABLE 5 Values of α₁ for NMEG drag-tags calculated from experimentaldata for ssDNA, taking into account the theory of end-effects. DNAlength (M_(C)) Drag-tag length (M_(U)) α₁ 20 20 0.19 40 0.21 40 20 0.2040 0.21Note that the closely spaced doublet for the arrival time of thesesingly labeled molecules was averaged for the results presented in Table5; using either the faster or slower times resulted in α₁ values thatdiffered from the average by a negligible amount. Note that the valuesof α₁ increase slightly with increasing size of the conjugate. For agiven class of polymer, α₁ is expected to be a constant that is relatedto the chemical structures of the components and the experimentalconditions (i.e. monomer size and Kuhn length, ionic strength of thebuffer). The slight variation among the conjugates is likely due to thefact that the DNA and the drag-tags are too small to be perfectlyGaussian in conformation, which is an underlying assumption for thetheory of ELFSE. Since the largest molecules are expected to be theclosest to being Gaussian in conformation, we use the correspondingvalue of α₁=0.21 to represent the true value for the poly(NMEG)drag-tags under the current experimental conditions.

Using the end-effect theory, the predicted arrival time for DNA with twodrag-tags is

$\begin{matrix}{t_{2} = \frac{t_{0}\left( {M_{c} + {2\alpha_{1}M_{u}}} \right)}{\int_{\alpha_{1}M_{u}}^{{\alpha_{1}M_{u}} + M_{c}}{{\Psi\left( \frac{n}{M_{c} + {2\alpha_{1}M_{u}}} \right)}{\mathbb{d}n}}}} & (14)\end{matrix}$Equations (13) and (14) can now be used to predict the ratio of themobilities of a bioconjugate with two drag-tags to the mobility of aconjugate with one drag-tag of twice the size, μ₂/μ₁=t₁/t₂. The valuespredicted from Equations (13) and (14), using α₁=0.21, are given inTable 6, along with the experimentally observed values, for the cases of20mer or 40mer DNA with either a single 40mer drag-tag, or two 20merdrag-tags.

TABLE 6 Mobility ratio μ₂/μ₁ for two 20mer drag-tags (μ₂) versus one40mer drag-tag (μ₁). DNA length (M_(C)) Predicted μ₂/μ₁ Experimentalμ₂/μ₁ 20 1.08 1.03 40 1.05 1.03The experimental results are closer to the value of 1, which is thatpredicted by the simple theory in Equation (2) that neglectsend-effects. The experimental value for the 40mer DNA is closer to thevalues predicted by the end-effect theory; this may be because thelarger chains more closely approximate Gaussian coils, and are thus moreappropriate test cases for the theory.

The quantitative end-effect theory is not directly applicable to thedsDNA data presented here. Although the dsDNA products are significantlylonger, dsDNA is also considerably stiffer, with a much longerpersistence length than ssDNA. Thus, even the longer dsDNA products aremore likely to resemble stiff rods or cylinders, rather than randomcoils. Even with such a geometry, there is still likely an end-effect,which is dramatically illustrated by the experimental measurements of apresented in Table 4. Since the dsDNA-drag-tag conjugates are not likelyto even approximate Gaussian coils, application of the theory used forthe ssDNA conjugates is not appropriate.

The drag enhancement for placing a drag-tag at each end of dsDNA isnoticeably larger than was observed for placing a drag-tag at each endof ssDNA. This could simply be a function of the specific sizes of DNAand drag-tags that were chosen for study, but it may also be the resultof the stiff rod-like structure of the dsDNA. Because the dsDNAmolecules studied here are relatively short, the ends of the dsDNAmolecule are more often on the “outside” of the chain, as opposed to atrue Gaussian coil for which the chain ends may occupy positions in theinterior of the coil. In addition, there may be a greater degree ofhydrodynamic segregation between the rod-like dsDNA and the random coildrag-tags. Detailed theoretical analysis is required to determine ifthese simple arguments can explain the larger end-effect observed fordsDNA in these experiments.

The enhanced drag arising from placing a drag-tag at both ends of DNAleads to interesting new possibilities for sequencing and genotyping byELFSE. The separation capacity of ELFSE is tied directly to the amountof friction generated by the drag-tag, and previous efforts have beenfocused on creating larger drag-tags to generate more friction. Thepossibility of including a drag-tag at both ends extends the range ofseparations that are possible with existing drag-tags. This isparticularly important as the production of very large, totallymonodisperse protein polymer drag-tags has proven difficult [15, 24].

This application has provided verification of an important andinteresting prediction of the new theory of end-effects in ELFSEseparations. Using both custom-synthesized ssDNA oligonucleotides andlarger dsDNA products generated by PCR, labeled at one or both ends witha variety of drag-tags, it has been shown that the drag induced bylabeling both ends is more than double the drag arising from a singledrag-tag at one end, and is also larger than the drag that would arisefrom a single drag-tag of twice the size at one end. The effect issignificant, with drag (α) enhanced by 6-9% for the ssDNA and by 10-23%for the dsDNA in the size range tested with the available drag-tags.This enhanced drag from double end-labeling is useful for various typesof ELFSE separations such as DNA sequencing, which will requireincorporation of a drag-tag on each end of the ssDNA prior to analysis.

Example 13 Review of Preferred Methods of the Invention

For greater clarity, two preferred methods of the invention are reviewedwith reference to FIGS. 14 and 15.

FIG. 14 illustrates a method in which polymeric compounds are provided.In step 100 the polymeric compounds are modified by attaching a chemicalmoiety at or near each end of the polymeric compounds to generate doublyend labeled polymeric compounds. In step 101 the double end labeledpolymeric compounds are subjected to free-solution electrophoresis,thereby to cause separation thereof.

FIG. 15 illustrates a method for DNA sequencing, which involves in step200 synthesizing a plurality of ssDNA molecules each comprising asequence identical to at least a portion of a section of DNA, each ssDNAhaving a length corresponding to a position of a specific nucleotide inthe sequence of the section of DNA. Subsequently, the ssDNAs aremodified in step 201 to attach a chemical moiety at or near each endthereof. The doubly end labeled ssDNAs san then be subjected in step 202to free-solution electrophoresis, thereby to cause separation thereof.In step 203 the nucleotide sequence can be identified by comparing therelative mobility of the doubly end labeled DNAs.

While the invention has been described with reference to particularpreferred embodiments thereof, it will be apparent to those skilled inthe art upon a reading and understanding of the foregoing that numerousmethods for polymeric compound modification and separation other thanthe specific embodiments illustrated are attainable, which nonethelesslie within the spirit and scope of the present invention. It is intendedto include all such designs, assemblies, assembly methods, andequivalents thereof within the scope of the appended claims.

REFERENCES

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1. A method for separating single-stranded polymeric compounds accordingto their relative molecular lengths, the method comprising: attaching achemical moiety at or near each end of each of said single-strandedpolymeric compounds to generate doubly end-labeled polymeric compounds;and subjecting the doubly end-labeled polymeric compounds tofree-solution electrophoresis, each chemical moiety suitable to impartincreased hydrodynamic friction to each end of each doubly end-labeledpolymeric compound thereby to facilitate separation of the doublyend-labeled polymeric compounds according to their electrophoreticmobilities during said free-solution electrophoresis.
 2. The method ofclaim 1, wherein the single-stranded polymeric compounds to be separatedare linear polymeric compounds.
 3. The method of claim 1, wherein thesingle-stranded polymeric compounds to be separated are chargedpolymeric compounds.
 4. The method of claim 1, wherein the chemicalmoieties attached as end-labels are uncharged or substantially unchargedchemical moieties.
 5. The method of claim 1, wherein the single-strandedpolymeric compounds to be separated are selected from among polypeptidesor polynucleotides.
 6. The method of claim 5, wherein thesingle-stranded polymeric compounds to be separated are selected fromamong the polynucleotides, including single-stranded DNA, and RNA. 7.The method of claim 1, wherein the chemical moieties attached asend-labels are selected from polypeptides, polypeptoids, andpolypeptide-polypeptoid conjugates.
 8. The method according to claim 1,wherein the chemical moieties are selected from the group consisting ofStreptavidin, or a derivative thereof, N-methoxyethylglycine(NMEG)-based polymers of length up to 3100 monomer units, and a moleculeconsisting of a poly(NMEG) backbone optionally grafted with oligo (NMEG)branches.
 9. A method for sequencing a section of a DNA molecule themethod comprising: (a) synthesizing a first plurality of ssDNA moleculeseach comprising a sequence identical to at least a portion at or nearthe 5′ end of slid section of DNA, said ssDNA molecules havingsubstantially identical 5′ ends but having variable lengths, the lengthof each ssDNA molecule corresponding to a specific adenine base in saidsection of DNA; (b) synthesizing a second plurality of ssDNA moleculeseach comprising a sequence identical to at least a portion at or nearthe 5′ end of said section of DNA, said ssDNA molecules havingsubstantially identical 5′ ends but having variable lengths, the lengthof each ssDNA molecule corresponding to a specific cytosine base in saidsection of DNA; (c) synthesizing a third plurality of ssDNA moleculeseach comprising a sequence identical to at least a portion at or nearthe 5′ end of said section of DNA, said ssDNA molecules havingsubstantially identical 5′ ends but having variable lengths, the lengthof each ssDNA molecule corresponding to a specific guanine base in saidsection of DNA; (d) synthesizing a fourth plurality of ssDNA moleculeseach comprising a sequence identical to at least a portion at or nearthe 5′ end of aid section of DNA, said ssDNA molecules havingsubstantially identical 5′ ends but having variable lengths, the lengthof each ssDNA molecule corresponding to a specific thymine base in saidsection of DNA; (e) attaching a chemical moiety to end nucleotides at ornear each end of said ssDNA molecules to generate doubly end-labeledpolymeric compounds; and (f) subjecting each plurality of ssDNAmolecules to free-solution electrophoresis; and (g) identifying thenucleotide sequence of the section of DNA in accordance with therelative electrophoretic mobilities of the ssDNAs in each plurality ofssDNAs; wherein any of steps (a), (b), (c), and (d) may be performed inany order or simultaneously; and whereby each chemical moiety impartsincreased hydrodynamic friction to each end of each doubly end-labeledpolymeric compound thereby to facilitate separation of the doublyend-labeled polymeric compounds according to their electrophoreticmobility.
 10. The method of claim 9, wherein the chemical moieties areuncharged chemical moieties.
 11. The method of claim 9, wherein thechemical moieties are selected from among polypeptides and polypeptoids.12. The method of claim 9, wherein the chemical moieties are selectedfrom the group consisting of Streptavidin, or a derivative thereof,N-methoxyethylglycine (NMEG) based polymers comprising up to 300 monomerunits, and a molecule consisting of a poly(NMEG) backbone optionallygrafted with oligo (NMEG) branches.
 13. The method according to claim 9,wherein the section of DNA comprises less than 2000 nucleotides.
 14. Themethod according to claim 13, wherein the section of DNA comprises lessthan 1000 nucleotides.
 15. The method according to claim 14, wherein thesection of DNA comprises less than 500 nucleotides.
 16. The methodaccording to claim 15, wherein the section of DNA comprises less than300 nucleotides.
 17. The method according to claim 16, wherein thesection of DNA comprises less than 100 nucleotides.
 18. A method forseparating single-stranded polymeric compounds differentiated in size byat least one polymer unit, the method comprising: attaching a chemicalmoiety at or near each end of the single-stranded polymeric compounds;and subjecting the single-stranded polymeric compounds with the attachedchemical moieties to free-solution electrophoresis, each chemical moietyimparting increased hydrodynamic friction to each end of said polymericcompounds to thereby modify the electrophoretic mobility of saidsingle-stranded polymeric compounds.
 19. The method of claim 18, whereinthe difference in relative size of the single-stranded polymericcompounds is a single polymer unit.
 20. The method of claim 19, whereinthe single-stranded polymeric compounds comprise single-stranded DNAmolecules, and each polymer unit is a nucleotide.